the smooth boundary as the minimiser of |V - V0|^2 + alpha |L V|^2, where L V is how far a vertex sits off the line through its neighbours. There is no iteration count: the minimiser is the solution of one sparse system, so the result depends on alpha alone. smoothingLength specifies the spatial wavelength damped to half amplitude. The weight alpha is derived from this length and the vertex spacing, so the smoothing scale remains comparable between samplings. Supplying alpha overrides that conversion.

Input

smoothingLength spatial wavelength damped to half amplitude, in the units of the boundary
alpha dimensionless regularisation weight, overriding smoothingLength

Members

smooth the minimiser of |V - V0|^2 + alpha |L V|^2 over the free vertices, one sparse system

Used on

GrainSmoothing, GrainSmoothingAdvanced

MATLAB’s curvatureFilter

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/curvatureFilter_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX 
@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.